# छत की ढाल कैलकुलेटर: कोण, प्रतिशत और उठान

> ऊर्ध्व उठान और क्षैतिज दूरी से कोण, प्रतिशत ढाल और छत का झुकाव (12 में x) निकालें। तिरछी लंबाई और राफ्टर गुणक भी देखें।

इंटरैक्टिव संस्करण: https://www.calcopenly.com/hi/geometry/slope-roof-pitch-calculator
विषय: ज्यामिति कैलकुलेटर

Every way of stating a slope comes from one ratio, m = rise ÷ run. The angle from horizontal is arctan m, the percent grade is 100m, the roof pitch is 12m (units of rise per 12 of run), and the rafter factor √(1 + m²) turns a horizontal run into the sloped length. Enter a rise and run, or any one of the other forms, and the rest follow.

The default rise of 6 over a run of 12 is a 6/12 roof: 26.57°, a 50% grade and a rafter factor of 1.1180, so 12 cm of run needs 13.4164 cm of rafter. Ramps and roads use the same numbers: the steepest ramp the 2010 ADA Standards allow, 1:12, is an 8.33% grade, or 4.76°.

Percent grade is not an angle: a 100% grade is 45°, and a vertical face has no finite grade or pitch, so angles must lie between −90° and 90°. A negative rise describes a downhill slope.

## इनपुट

- **ज्ञात माप** (विकल्प: Rise and run, कोण, Percent grade, Roof pitch)
- **Rise**: Negative for a downhill slope
- **Run (horizontal distance)**
- **Angle from horizontal**: Between −90° and 90°
- **ग्रेड**: Rise per 100 of run
- **Pitch**: Rise for every 12 of run, as in a 6/12 roof
- **परिणाम की इकाई** (विकल्प: मिलीमीटर (mm), सेंटीमीटर (cm), मीटर (m), किलोमीटर (km), इंच (in), फुट (ft), गज (yd), मील (mi))

## नतीजे

- कोण (°) — मुख्य परिणाम
- ग्रेड
- Roof pitch (in 12)
- Ratio (rise : run)
- Rise per unit of run
- Rafter length factor
- Slope length

## सूत्र

$$
\begin{gathered} m = \frac{\text{rise}}{\text{run}},\quad \theta = \arctan m,\quad \text{grade} = 100m\,\% \\[6pt] \text{pitch} = 12m \text{ in } 12,\quad \text{factor} = \sqrt{1 + m^2} \end{gathered}
$$

## हल किए गए उदाहरण

### Rise 6, run 12 (a 6/12 roof)

- ज्ञात माप: Rise and run
- Rise: 6 cm
- Run (horizontal distance): 12 cm
- परिणाम की इकाई: सेंटीमीटर (cm)
- **कोण: 26.565051 °**
- **ग्रेड: 50%**
- **Roof pitch: 6 in 12**
- **Ratio (rise : run): 1 : 2**
- **Rafter length factor: 1.118034**
- **Slope length: 13.416408 cm**
- जाँच का स्रोत: Python 3.8 math: degrees(atan(0.5)), sqrt(1.25), sqrt(6**2 + 12**2)

### 45°

- ज्ञात माप: कोण
- Angle from horizontal: 45 °
- **ग्रेड: 100%**
- **Roof pitch: 12 in 12**
- **Ratio (rise : run): 1 : 1**
- **Rafter length factor: 1.414214**
- जाँच का स्रोत: tan 45° = 1; Python 3.8 math.sqrt(2)

### 8 % road grade

- ज्ञात माप: Percent grade
- ग्रेड: 8%
- **कोण: 4.573921 °**
- **Roof pitch: 0.96 in 12**
- **Ratio (rise : run): 1 : 12.5**
- जाँच का स्रोत: Python 3.8 math: degrees(atan(0.08)); 12 × 0.08; 1/0.08

### 4/12 roof pitch

- ज्ञात माप: Roof pitch
- Pitch: 4 in 12
- **कोण: 18.434949 °**
- **ग्रेड: 33.333333%**
- **Rafter length factor: 1.054093**
- जाँच का स्रोत: Python 3.8 math: degrees(atan(4/12)), sqrt(1 + 1/9)

### ADA ramp 1:12

- ज्ञात माप: Rise and run
- Rise: 1 cm
- Run (horizontal distance): 12 cm
- परिणाम की इकाई: सेंटीमीटर (cm)
- **ग्रेड: 8.333333%**
- **कोण: 4.763642 °**
- **Ratio (rise : run): 1 : 12**
- जाँच का स्रोत: ADA §405.2 maximum ramp slope 1:12; Python 3.8 math: degrees(atan(1/12))

### Flat ground (edge case)

- ज्ञात माप: Rise and run
- Rise: 0 cm
- Run (horizontal distance): 5 cm
- परिणाम की इकाई: सेंटीमीटर (cm)
- **कोण: 0 °**
- **ग्रेड: 0%**
- **Roof pitch: 0 in 12**
- **Rafter length factor: 1**
- **Slope length: 5 cm**
- जाँच का स्रोत: Zero rise: tan θ = 0

## सवाल

### How do you convert percent grade to degrees?

Take the arctangent of the grade divided by 100: θ = arctan(grade/100). An 8% road grade is arctan 0.08 = 4.57°, and a 100% grade is 45°, not 90°. The reverse is grade = 100 × tan θ, so a 30° slope is a 57.7% grade.

### What angle is a 6/12 roof pitch?

26.57°. A pitch of x/12 means x units of rise for every 12 of run, so the angle is arctan(x/12): 4/12 is 18.43°, 6/12 is 26.57°, 8/12 is 33.69° and 12/12 is 45°. The rafter factor for 6/12 is √1.25 = 1.118, so 12 ft of horizontal run needs 13.42 ft of rafter before any overhang.

### What is the maximum slope for a wheelchair ramp?

1:12 under the 2010 ADA Standards for Accessible Design (§405.2): one unit of rise for every 12 of run, an 8.33% grade or 4.76°. Each ramp run may rise at most 30 in (§405.6), so a 30 in rise needs a run of at least 30 ft. Other countries set their own limits in their building codes.

### How do you calculate rise over run?

Divide the vertical rise by the horizontal run, both in the same unit: m = rise/run. A roof that rises 6 in over 12 in of run has m = 0.5. Measure the run horizontally, not along the surface: the sloped length here is 13.42 in, and dividing by it gives 0.447, the sine of the angle rather than the slope.

### “छत की ढाल कैलकुलेटर: कोण, प्रतिशत और उठान” कितना सटीक है?

सटीकता आपके इनपुट और विधि की मान्यताओं पर निर्भर करती है। दशमलव गणना 50 सार्थक अंकों का उपयोग करती है, लेकिन अनुमान, संख्यात्मक विधियाँ और स्रोत डेटा कम सटीक हो सकते हैं। दिखाए गए मानों को पूर्णांकित करने से ये सीमाएँ दूर नहीं होतीं। स्वतंत्र स्रोतों के हल किए गए उदाहरणों से जाँच: 8। उदाहरण के लिए, “Rise 6, run 12 (a 6/12 roof)” की जाँच Python 3.8 math: degrees(atan(0.5)), sqrt(1.25), sqrt(6**2 + 12**2) से की गई है।

### इस विधि का स्रोत क्या है?

OpenStax College Algebra 2e, §4.1 — slope as rise over run; US Access Board, ADA Standards §405.2 — ramp slope 1:12 (8.33 %).

## स्रोत

- [OpenStax College Algebra 2e, §4.1 — slope as rise over run](https://openstax.org/books/college-algebra-2e/pages/4-1-linear-functions)
- [US Access Board, ADA Standards §405.2 — ramp slope 1:12 (8.33 %)](https://www.access-board.gov/ada/#ada-405)